1
|
Bachhar A, Mayhall NJ. Restricted Open-Shell Cluster Mean-Field theory for Strongly Correlated Systems. J Phys Chem A 2024; 128:9015-9027. [PMID: 39373627 PMCID: PMC11492245 DOI: 10.1021/acs.jpca.4c03914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2024] [Revised: 09/20/2024] [Accepted: 09/20/2024] [Indexed: 10/08/2024]
Abstract
The cluster-based Mean Field method (cMF) and it is second order perturbative correction was introduced by Jiménez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small clusters, which are individually solved in the mean-field presence of each other. In that work, clusters with unpaired electrons are treated by allowing the α and β orbitals to spin polarize. While that provided significant energetic stabilization, the resulting cMF wave function was spin-contaminated, making it difficult to use as a reference state for spin-pure post-cMF methods. In this work, we propose the Restricted Open-shell cMF (RO-cMF) method, extending the cMF approach to systems with open-shell clusters, while not permitting spin-polarization. While the resulting RO-cMF energies are necessarily higher in energy than the unrestricted orbital cMF, the new RO-cMF provides a simple reference state for post-cMF methods that recover the missing intercluster correlations. We provide a detailed explanation of the method, and report demonstrative calculations of exchange coupling constants for three systems: a di-iron complex, a dichromium complex, and a dimerized organic radical. We also report the first perturbatively corrected RO-cMF-PT2 results as well.
Collapse
Affiliation(s)
- Arnab Bachhar
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
- Virginia
Tech Center for Quantum Information Science and Engineering, Blacksburg, Virginia 24061, United States
| | - Nicholas J. Mayhall
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
- Virginia
Tech Center for Quantum Information Science and Engineering, Blacksburg, Virginia 24061, United States
| |
Collapse
|
2
|
Braunscheidel NM, Bachhar A, Mayhall NJ. Accurate and interpretable representation of correlated electronic structure via Tensor Product Selected CI. Faraday Discuss 2024. [PMID: 39119803 DOI: 10.1039/d4fd00049h] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/10/2024]
Abstract
The task of computing wavefunctions that are accurate, yet simple enough mathematical objects to use for reasoning, has long been a challenge in quantum chemistry. The difficulty in drawing physical conclusions from a wavefunction is often related to the generally large number of configurations with similar weights. In Tensor Product Selected Configuration Interaction (TPSCI), we use a locally correlated tensor product state basis, which has the effect of concentrating the weight of a state onto a smaller number of physically interpretable degrees of freedom. In this paper, we apply TPSCI to a series of three molecular systems ranging in separability, one of which is the first application of TPSCI to an open-shell bimetallic system. For each of these systems, we obtain accurate solutions to large active spaces, and analyze the resulting wavefunctions through a series of different approaches including (i) direct inspection of the TPS basis coefficients, (ii) construction of Bloch effective Hamiltonians, and (iii) computation of cluster correlation functions.
Collapse
Affiliation(s)
| | - Arnab Bachhar
- Department of Chemistry, Virginia Tech, Blacksburg, VA 24060, USA.
| | | |
Collapse
|
3
|
Agarawal V, King DS, Hermes MR, Gagliardi L. Automatic State Interaction with Large Localized Active Spaces for Multimetallic Systems. J Chem Theory Comput 2024; 20:4654-4662. [PMID: 38787596 DOI: 10.1021/acs.jctc.4c00376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2024]
Abstract
The localized active space self-consistent field method factorizes a complete active space wave function into an antisymmetrized product of localized active space wave function fragments. Correlation between fragments is then reintroduced through localized active space state interaction (LASSI), in which the Hamiltonian is diagonalized in a model space of LAS states. However, the optimal procedure for defining the LAS fragments and LASSI model space is unknown. We here present an automated framework to explore systematically convergent sets of model spaces, which we call LASSI[r, q]. This method requires the user to select only r, the number of electron hops from one fragment to another, and q, the number of fragment basis functions per Hilbert space, which converges to CASCI in the limit of r, q → ∞. Numerical tests of this method on the trimetal oxo-centered complexes [Fe(III)Al(III)Fe(II)(μ3-O)(HCOO)6] and [Fe(III)2Fe(II)(μ3-O)(HCOO)6] show efficient convergence to the CASCI limit with 4-10 orders of magnitude fewer states than CASCI.
Collapse
Affiliation(s)
- Valay Agarawal
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Daniel S King
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Matthew R Hermes
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Laura Gagliardi
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| |
Collapse
|
4
|
Papastathopoulos-Katsaros A, Henderson TM, Scuseria GE. Linear Combinations of Cluster Mean-Field States Applied to Spin Systems. J Chem Theory Comput 2024; 20:3697-3705. [PMID: 38695526 DOI: 10.1021/acs.jctc.4c00171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2024]
Abstract
We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field states and apply it to describe the ground state of strongly correlated spin systems. In cluster mean-field theory, the ground state wave function is expressed as a factorized tensor product of optimized cluster states. While our prior work concentrated on a single cMF tiling, this study removes that constraint by combining different tilings of cMF states. Selection criteria, including translational symmetry and spatial proximity, guide this process. We present benchmark calculations for the one- and two-dimensional J1 - J2 and XXZ Heisenberg models. Our findings highlight two key aspects. First, the method offers a semiquantitative description of the 0.4 ≲ J2/J1 ≲ 0.6 regime of the J1 - J2 model─a particularly challenging regime for existing methods. Second, our results demonstrate the capability of our method to provide qualitative descriptions for all the models and regimes considered, establishing it as a valuable reference. However, the inclusion of additional (weak) correlations is necessary for quantitative agreement, and we explore methods to incorporate these extra correlations.
Collapse
Affiliation(s)
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| |
Collapse
|
5
|
Braunscheidel NM, Abraham V, Mayhall NJ. Generalization of the Tensor Product Selected CI Method for Molecular Excited States. J Phys Chem A 2023; 127:8179-8193. [PMID: 37733948 DOI: 10.1021/acs.jpca.3c03161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/23/2023]
Abstract
In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited-state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons with respect to the extrapolated result (i.e., near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.
Collapse
Affiliation(s)
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| |
Collapse
|
6
|
Papastathopoulos-Katsaros A, Henderson TM, Scuseria GE. Symmetry-projected cluster mean-field theory applied to spin systems. J Chem Phys 2023; 159:084107. [PMID: 37610020 DOI: 10.1063/5.0155765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2023] [Accepted: 07/11/2023] [Indexed: 08/24/2023] Open
Abstract
We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 - J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.
Collapse
Affiliation(s)
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| |
Collapse
|
7
|
Zhang H, Zou J, Ren X, Li S. Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems. J Phys Chem Lett 2023:6792-6799. [PMID: 37478417 DOI: 10.1021/acs.jpclett.3c01474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/23/2023]
Abstract
An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. For a water hexamer with stretched O-H bonds, which is beyond the capability of the CASSCF method, EOM-GVB-BCCC2b provides very close results as the density matrix renormalization group (DMRG). For four conjugated diradical species with triplet ground states, we found that their vertical S-T gaps from EOM-GVB-BCCC2b are also quite consistent with the DMRG results. This new method is expected to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.
Collapse
Affiliation(s)
- Haodong Zhang
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Jingxiang Zou
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Xiaochuan Ren
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| |
Collapse
|
8
|
Otten M, Hermes MR, Pandharkar R, Alexeev Y, Gray SK, Gagliardi L. Localized Quantum Chemistry on Quantum Computers. J Chem Theory Comput 2022; 18:7205-7217. [PMID: 36346785 PMCID: PMC9753592 DOI: 10.1021/acs.jctc.2c00388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2022] [Indexed: 11/09/2022]
Abstract
Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here, we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground-state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with the system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene, and resource estimates are provided for linear chains of up to 20 H2 molecules.
Collapse
Affiliation(s)
- Matthew Otten
- HRL
Laboratories, LLC, 3011
Malibu Canyon Road, Malibu, California90265, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States
| | - Riddhish Pandharkar
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States
| | - Yuri Alexeev
- Computational
Science Division, Argonne National Laboratory, Lemont, Illinois60439, United States
| | - Stephen K. Gray
- Center
for Nanoscale Materials, Argonne National
Laboratory, Lemont, Illinois60439, United
States
| | - Laura Gagliardi
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States
- Argonne
National Laboratory, Lemont, Illinois60439, United States
| |
Collapse
|
9
|
Zou J, Wang Q, Ren X, Wang Y, Zhang H, Li S. Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems. J Chem Theory Comput 2022; 18:5276-5285. [PMID: 35922401 DOI: 10.1021/acs.jctc.2c00445] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu2O2]2+ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C-C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.
Collapse
Affiliation(s)
- Jingxiang Zou
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Qingchun Wang
- Key Laboratory of Quantum Information, Chinese Academy of Sciences, School of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Xiaochuan Ren
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Yuqi Wang
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Haodong Zhang
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Shuhua Li
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| |
Collapse
|
10
|
Abraham V, Mayhall NJ. Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions. J Chem Theory Comput 2022; 18:4856-4864. [PMID: 35878319 DOI: 10.1021/acs.jctc.2c00589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH4 and F2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.
Collapse
Affiliation(s)
- Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| |
Collapse
|